Cryptology ePrint Archive: Report 2009/612

On the Impossibility of Batch Update for Cryptographic Accumulators

Philippe Camacho

Abstract: A cryptographic accumulator is a scheme where a set of elements is represented by a single short value. This value, along with another value called witness allows to prove membership into the set. In their survey on accumulators [FN02], Fazzio and Nicolisi noted that the Camenisch and Lysyanskaya's construction[CL02] was such that the time to update a witness after m changes to the accumulated value was proportional to m. They posed the question whether batch update was possible, namely if it was possible to build a cryptographic
accumulator where the time to update witnesses is independent from the number of changes in the accumulated set.
Recently, Wang et al. answered positively by giving a construction for an accumulator with batch update in [WWP07, WWP08]. In this work we show that the construction is not secure by exhibiting an attack. Moreover, we prove it cannot be fixed. If the accumulated value has been updated m times, then the time to update a witness must be at least
(m) in the worst case.